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This article focuses on the study of heat and mass transfer (HMT) fluid flow over an exponentially accelerated vertical plate, which is subjected to an applied magnetic field and viscous dissipation. The research has applications in various manufacturing processes such as wire/fiber drawing, hot rolling, continuous casting, and hot extrusion, where heat transfer to the ambient medium and the hot moving material are of utmost importance. The findings could also be relevant to aerospace engineering applications. The study investigates the time‐fractional natural convection phenomenon and utilizes conservation laws to derive the flow guiding equations, which are then made nondimensional. Finite difference discretization is utilized to solve the dimensionless equations implicitly. Then the flow simulation results such as concentration, temperature, and velocity profiles are discussed based on the variation in parameters such as Prandtl number (Pr $Pr$), thermal/mass Grashof number (Gr/Gc ${Gr}/{Gc}$), Eckert number (Ec ${Ec}$), magnetic parameter (M $M$), time‐fractional order (λ $\lambda $), and Schmidt number (Sc) $({Sc})$. Also, the HMT rate is depicted using the Nusselt number and skin friction plots. It is noted that HMT increases when Sc ${Sc}$ increases and λ $\lambda $ decreases. The change in time‐fractional order affects the velocity profiles adjacent to the wall and is more significant in the case of lower values of the Prandtl number. [ABSTRACT FROM AUTHOR]

This paper deals with the numerical solution of space fractional Burger's equation using the implicit finite difference scheme and Lax-Friedrichs- implicit finite difference scheme respectively. The Riemann-Liouville based fractional derivative (non-integer order) is fitted for the diffusion term of fractional order 1:0 < α ≤ 2:0. The Mathematical induction is used to es- timate a stability of both the implicit and Lax-Friedrichs-implicit schemes. The study shows that the implicit based scheme is stable and the results are good in agreement with the exact solution. Finally, the significance of space fractional order with respect to the solution is discussed. It is noted that the solution of space fractional Burger's equation get affected by changing the space fractional order. [ABSTRACT FROM AUTHOR]

A study is conducted to inspect the flow characteristics of a hybrid nanofluid over a vertical plate under the influence of magnetohydrodynamic free convection by considering chemical reaction, diffusion-thermo, thermal diffusion, thermal radiation, and viscous dissipation. However, the effects of Hall current and ion-slip were neglected. The flow of a hybrid nanofluid is considered to occur in a porous medium. To describe the flow, a set of ruling governing equations is generated in conjunction with conservation laws. The derived ruling equations were non-dimensionalized using various dimensionless parameters and variables. The obtained dimensionless form of equations was then solved numerically with the help of FORTRAN algorithm. The results were retrieved in terms of velocity, temperature, concentration, Nusselt number, skin friction, and Sherwood number. Also, the study aimed to compare the heat and mass transfer behavior of various Cu-water-based hybrid nanoliquids. In this regard, Al2O3-Cuwater, Ag-Cu-water, MWCNT-Cu-water, and TiO2-Cu-water hybrid nanofluid flow's heat and mass transfer rates were analyzed. [ABSTRACT FROM AUTHOR]

In this paper, a numerical study of time-fractional based Burgers' equation (TFBE) by using Caputo fractional derivatives (CFD), Caputo-Fabrizio fractional derivatives (CFFD), and Atangana-Baleanu fractional derivatives (ABFD) is carried out. The TFBE is solved using an implicit upwind scheme based on the finite difference method (IFDM). After verifying the IFDM scheme against the stability and convergence, the numerical solutions that are derived and validated with the exact solution and also compared with the CFD, CFFD, and ABFD models. [ABSTRACT FROM AUTHOR]